$g(t) = 3t^{2}-7t+2-2(f(t))$ $f(x) = -3x-1$ $ f(g(-7)) = {?} $
Solution: First, let's solve for the value of the inner function, $g(-7)$ . Then we'll know what to plug into the outer function. $g(-7) = 3(-7)^{2}+(-7)(-7)+2-2(f(-7))$ To solve for the value of $g$ , we need to solve for the value of $f(-7)$ $f(-7) = (-3)(-7)-1$ $f(-7) = 20$ That means $g(-7) = 3(-7)^{2}+(-7)(-7)+2+(-2)(20)$ $g(-7) = 158$ Now we know that $g(-7) = 158$ . Let's solve for $f(g(-7))$ , which is $f(158)$ $f(158) = (-3)(158)-1$ $f(158) = -475$